6406
J. Phys. Chem. A 2000, 104, 6406-6410
Kinetic Study of the Reactions of Ca(1S) and Sr(1S) Atoms with Cl2 in the Temperature Ranges from Respectively 303-1038 K and 303-991 K Chris Vinckier,* Joe1 lle Helaers, and Jan Remeysen Department of Chemistry, KU LeuVen, Celestijnenlaan 200F, 3001 HeVerlee, Belgium ReceiVed: January 14, 2000; In Final Form: April 21, 2000
1 A kinetic investigation of the second-order reactions Ca(1S) + Cl2(1Σ+ g ) f(k1Ca) CaCl + Cl and Sr( S) + + 1 Cl2( Σg ) f(k1Sr) SrCl + Cl was carried out in a fast-flow reactor in the temperature ranges of respectively 303-1038 K and 303-991 K. The calcium and strontium atoms in the gas phase were generated by thermal evaporation of the solid metal pellets. The concentration of the gas-phase metal atoms was followed by means of atomic absorption spectroscopy (AAS) at wavelengths of 422.7 nm for calcium and 460.7 nm for strontium atoms. Both reactions show an Arrhenius behavior and the rate constants are given by k1Ca ) [(6.0 ( 0.8) × 10-10]exp(-0.2 ( 0.5 kJ mol-1/RT)cm3 molecule-1 s-1 and k1Sr ) [(7.3 ( 0.6) × 10-10]exp(-0.4 ( 0.4 kJ mol-1/RT)cm3 molecule-1 s-1. The results are interpreted in terms of the electron-jump mechanism. For both the Ca/Cl2 and the Sr/Cl2 reactions, the experimental rate constants are too high to be quantitatively explained by the classical electron-jump mechanism. However, the modified electron-jump mechanism which takes into account long distance forces between the reagents gives a better agreement with the experimental values.
Introduction
following expressions:
The classic collision theory states that a reaction can only occur when the solid sphere of reagent A with a diameter σA collides with the solid sphere of reaction partner B with a diameter σB. A necessary condition for having a reactive collision is that the centers of gravity of both reacting species approach to each other until a distance rA-B equal to (σA + σB)/2 is reached. The maximum cross-section Qr for this reactive process can be expressed as π(rA-B)2. However, for the alkalinemetal atom/halogen reactions extremely high values for Qr were experimentally determined, which could not be explained on the basis of the classic collision theory. Indeed gas collision cross sections in the range of 30-50 Å2 can be expected while for the alkaline-metal atom reactions cross sections with Cl2, Br2 and I2 between 100 and 200 Å2 have been measured.1-5 Apparently such reactions do not require a classic collision between both reaction partners and they could better be treated by the so-called electron-jump or harpooning mechanism.6-7 It needs to be pointed out that the closed-shell character of the alkaline-earth-metal atoms may result in a potential energy barrier when the reagents approach each other under a number of geometrical configurations. Honjou and Yarkony8 indeed calculated a maximum energy barrier of 28.5 kJ mol-1 for the perpendicular C2V approach of the Ca atom toward the Cl2 molecule. They also demonstrated that in contrast to the C2V approach a collinear C∝V approach does not show an energy barrier. Up until now the reaction dynamics of a Cs approach have not been looked at, but one may assume that this reaction geometry will give an energy barrier intermediate between the two extreme situations (C2V and C∝V). In this paper a kinetic study will be presented on the Ca(Sr)/ Cl2 reactions. The only kinetic measurements available were obtained in atomic diffusion flames in the narrow temperature ranges between 933 and 1083 K.9 Both rate constants show a negative temperature dependence as can be seen from the
k1Ca ) [(2.0 ( 0.5) × 10-5]T-1.91(0.03 cm3 molecule-1 s-1 (1) k1Sr ) [(9.1 ( 0.3) × 10-14]T-0.50(0.02 cm3 molecule-1 s-1 (2) Another source of information on the Ca(Sr)/Cl2 reactions is coming from molecular beam experiments.10 From the angle dependence of the MeX product formation, it has been concluded that the reactions proceed through the formation of a very short-living intermediate complex, with a lifetime which is several times lower than its rotational period. More recently Gole et al.11 investigated the emission arising from the mixed halogen Sr/(Cl2,Br2) reactions using both chemiluminescent and LIF techniques.
Sr + (Cl2, Br2) f SrCl + SrBr
(3)
/† Sr + (Cl2, Br2) f SrCl/† 2 + SrBr2
(4a)
/ SrCl/† 2 + M f SrCl2 f SrCl2 + hν
(4b)
SrCl/2 + SrCl f SrCl2 + SrCl* f SrCl2 + SrCl + hν (4c) / SrBr/† 2 + M f SrBr2 f SrBr2 + hν
(4d)
SrBr/2 + SrBr f SrBr2 + SrBr* f SrBr2 + SrBr + hν (4e) The main reaction leads to nascent electronically excited /† SrCl/† 2 and SrBr2 dihalide products (4a). In a further step one gets collisional stabilization (M ) bath gas or so-called third body) to form the long-living SrCl/2 and SrBr/2 molecules (4b and 4d). Also the SrCl and SrBr monohalides were formed in the ground-state (3), which is not surprising since the reaction
10.1021/jp000212i CCC: $19.00 © 2000 American Chemical Society Published on Web 06/17/2000
Reactions of Ca(1S) and Sr(1S) Atoms with Cl2
J. Phys. Chem. A, Vol. 104, No. 27, 2000 6407
to electronically excited states of SrCl and SrBr are endothermic for respectively 10.8 and 34.7 kJ mol-1.12 However, emission from SrCl* and SrBr* has also been seen (4c and 4e), and this was explained by assuming an energy transfer in (4c) and (4e) from the electronically excited SrCl/2 and SrBr/2 to the groundstate monohalides formed in (3). Kinetic measurements on the Ca(1S) and Sr(1S) atom/Cl2 reactions will now be presented covering the temperature ranges from respectively 303-1038 K and 303-991 K. The experiments were carried out in a fast-flow reactor using AAS as the detection technique for the thermally evaporated alkaline-earthmetal atoms. The results will be discussed in terms of the electron-jump mechanism. Experimental Technique The experimental setup has been amply described in earlier publications,13-17 and only a brief summary will be presented here. It consists of two major parts: a fast-flow reactor under low pressure and an AAS detection technique. The fast-flow reactor consists of a quartz tube with an internal diameter of 5.7 cm and a length of 100 cm. At the upstream end a sample holder carried the metal pellets which were thermally evaporated at 600-700 K by means of a kanthal resistance wire. By means of the carrier gas helium, the alkaline-earth-metal atoms were transported downstream in the kinetic zone where they were mixed with an excess of Cl2. In the pressure range from 6 to 12 Torr, the flow velocity Vg of the carrier gas helium has a constant value of 320 ( 10 cm s-1 at 303 K. The temperature in the kinetic zone could be varied between 303 and 1000 K by means of an electrical oven and the temperature was monitored by a shielded chromel-alumel thermocouple. Calcium and strontium atoms were detected by AAS at respectively 422.7 and 460.7 nm. Assuming that the detection limit corresponds to an absorbance of A ) 0.005, one can calculate the detection limit for the Ca(Sr) atoms by using a formalism explained in an earlier paper:18 [Ca(Sr)] ) C1AL-1Tg1/2 in which C1 is a proportionality constant, L the optical path length (5.7 cm), and Tg the gas temperature. With values for C1(Ca) ) 0.663 × 1010 cm-2 K-1/2 and C1(Sr) ) 0.428 × 1010 cm-2 K-1/2 at 500 K,19 one can calculate the detection limits for calcium to be 1.3 × 108 atoms cm-3 or 1.12 ppb and for strontium: 8.4 × 107 atoms cm-3 or 0.72 ppb at 6 Torr and 500 K. Minimum distances between the metal atom source, the Cl2 inlet, and the kinetic zone were maintained to allow for sufficient mixing of the reagents as explained in earlier publications.16,17 Kinetic measurements were made by following the decay of the alkaline-earth-metal atom absorbance as a function of the axial distance along the fast-flow reactor. This was realized by moving the entire reactor assembly along its axis relative to the detection equipment which remained at a fixed position. Decays of the absorbances as a function of the distance can easily be transformed into decays as a function of the reaction time t using the expression t ) zd/Vg. An advantage of this technique is that relative positions of the metal atom source and the Cl2 inlet remain constant during the experiments. Reproducible absorbances could be maintained within 10% when the temperature Ts of the metal pellets was stabilized within ( 1%. For all the investigated reactions helium (L’Air Liquide) with a purity of 99.995% was used as a carrier gas as well as in the gas mixtures. The Cl2 concentration was equal to 0.075% of Cl2 for both the Ca/Cl2 and the Sr/Cl2 reactions. The calcium pellets (Fluka) and the strontium pellets (Aldrich) respectively had a purity of about 99.5% and 99.0%.
Figure 1. The natural logarithm of the Sr atom absorbance as a function of the reaction time t at various amounts of added Cl2. The experimental conditions are Tg ) 651 K, Pr ) 10 Torr. He as carrier gas. [Cl2] (9) 0, (0) 0, ([) 1.9, (]) 3.8, (b) 6.3, (O) 8.7, (2) 11.0, (4) 14.0, (+) 21.0, and (×) 23.0 expressed in units of 1010 molecules cm-3.
Figure 2. The slopes S of eq 5 for the Ca/Cl2 reaction as a function of the added Cl2 concentration. The experimental conditions are Tg ) 303 K ([) (Pr ) 8 Torr), 489 K (0) (Pr ) 10 Torr), and 930 K (b) (Pr ) 10 Torr). He as carrier gas, [Cl2] is expressed in units of 1010 molecules cm-3.
Weighted regressions on all plots were made using the statistical SAS package.20 The quoted errors σ were the standard deviations. Results Determination of the Rate Constants k1Ca and k1Sr. The kinetic formalism used in the derivation of the rate constants of the Ca(Sr)/Cl2 reactions has already been described in previous papers16,17
ln ACa(Sr) ) -
{
k1Ca(Sr)[Cl2] η
+
}
7.34DCa(Sr)/He 2r2
t+B
(5)
in which ln ACa(Sr) is the natural logarithm of respectively the calcium and strontium absorbance, η a correction factor depending on the flow characteristics, DCa(Sr)/He the binary diffusion coefficients of the Ca and Sr atoms in the carrier gas helium, r the reactor radius, t the reaction time, and B an integration constant. The correction factor η is related to the flow characteristics, and the determination of its magnitude has been amply discussed elsewhere.21 The use of eq 5 for obtaining kinetic parameters has been well-illustrated in our earlier work16,22 and will only briefly be summarized here. The values of the rate constants k1Ca(Sr) were
6408 J. Phys. Chem. A, Vol. 104, No. 27, 2000
Vinckier et al.
TABLE 1: The Rate Constants k1Ca(Sr) of the Reactions Ca(1S) + Cl2 and Sr(1S) + Cl2 as a Function of the Temperature Tga Tg (K)
Pr (Torr)
AiCa
k1Ca (× 10-10 cm3 molecule-1 s-1)
Tg (K)
Pr (Torr)
AiSr
k1Sr (× 10-10 cm3 molecule-1 s-1)
303 303 303 303 303 356 398 398 489 544 544 603 700 790 790 930 1038 1038
6 8 8 10 12 10 8 8 10 8 8 10 8 10 10 10 10 10
0.55 0.75 0.93 0.84 0.41 0.76 1.20 0.56 1.10 0.72 0.33 1.01 0.40 1.00 0.34 0.80 0.40 0.52
5.6 ( 0.5 4.9 ( 0.6 4.9 ( 0.3 5.9 ( 0.3 5.6 ( 0.5 5.3 ( 0.7 4.1 ( 0.6 5.3 ( 1.0 5.5 ( 0.7 4.5 ( 0.6 5.4 ( 0.7 7.7 ( 0.3 8.2 ( 1.1 5.7 ( 0.4 8.3 ( 0.4 6.4 ( 0.4 3.8 ( 0.3 4.5 ( 0.5
303 303 303 303 303 303 352 393 449 507 554 598 651 651 651 651 651 707 753 791 822 822 888 991
6 6 8 8 10 12 8 8 8 8 8 8 6 8 10 11 12 8 8 8 8 8 8 8
0.29 0.33 0.47 0.36 0.46 0.52 0.31 0.13 0.27 0.33 0.19 0.18 0.16 0.15 0.36 0.19 0.10 0.07 0.15 0.49 0.12 0.40 0.13 0.10
6.8 ( 1.1 6.6 ( 0.9 4.4 ( 1.0 6.7 ( 0.9 5.7 ( 0.9 4.7 ( 0.6 6.4 ( 0.3 6.4 ( 0.9 5.3 ( 0.7 6.5 ( 0.4 6.0 ( 0.9 5.8 ( 0.2 8.1 ( 1.4 8.0 ( 0.4 8.4 ( 0.3 8.0 ( 0.4 7.4 ( 0.3 5.7 ( 0.4 7.8 ( 0.4 5.9 ( 0.9 8.2 ( 0.3 7.1 ( 1.0 5.7 ( 0.2 6.7 ( 0.2
a
i Pr is the reactor pressure, and ACa(Sr) is the initial absorbance.
determined by following first ln ACa(Sr) as a function of the reaction time t at various amounts of Cl2 added. Then a weighted linear regression of ln ACa(Sr) versus t was performed, in which each value of ln ACa(Sr) had a weighting factor equal to 1/σ2ln A. As an example, the pseudo-first-order decays of Sr(1S) atoms as a function of the reaction time t for various initial Cl2 concentrations at a temperature Tg ) 651 K and a pressure Pr equal to 10 Torr are shown in Figure 1. In the next step, the slopes S of these lines were plotted versus the added [Cl2] and a weighted linear regression resulted in a straight line with a slope equal to k1Ca(Sr)/η as is illustrated in Figure 2 for three different temperatures: 303, 489, and 930 K for the Ca/Cl2 reaction. Finally the observed slopes in Figure 2 need to be multiplied by η to obtain the correct second-order rate constants k1Ca(Sr). The value of η depends on the magnitude of the intercept and the procedure to determine its value is the same as in a previous paper on the Mg(Ca,Sr)/NO2 reactions.23 In the given examples for the Ca/Cl2 reaction values for the second-order rate constants k1Ca ) 4.9 ( 0.6 (303 K), 5.5 ( 0.7 (489 K) and 6.4 ( 0.4 (930 K) in units of 10-10 cm3 molecule-1 s-1 were obtained. To confirm the second-order behavior of the reactions, the pressure dependence of the rate constants k1Ca(Sr) was examined in the pressure range between 6 and 12 Torr and this at various temperatures between 303 and 651 K. It was indeed found that the obtained values of k1Ca(Sr) were independent of the pressure. This also confirms that hydrodynamic effects, as there are the mixing of the reagents or the wall-loss of Ca(Sr) atoms, have no systematic effect on the derived values of k1Ca(Sr). The influence of the initial alkaline-earth-metal atom concentration on the value of k1Ca(Sr) has been checked. For this i was varied with a factor of 2 to 3.5 and in none purpose, ACa(Sr) of the cases any systematic effect on k1Ca(Sr) was noticed. This proves that, as expected at these low initial metal atom concentrations, mutual reactions between the metal atoms or consecutive reaction steps involving these metal atoms could be neglected. Temperature Dependence of k1Ca and k1Sr. To establish the temperature dependence of the rate constants k1Ca(Sr), experiments
Figure 3. Plot of ln k1Ca(Sr) versus 1/T according to the weighted nonlinear regression method: Ca/Cl2 ([) (s) (eq 7) and Sr/Cl2 (O) (s s) (eq 8).
TABLE 2: Reaction Enthalpy ∆HR (kJ mol-1) of the Ca(Sr)/Cl2 Reactions Leading to Various Electronic States of the Corresponding Metal Chloride MeCl12 electronic states of the MeCl product
Ca
Sr
X2Σ+ A2Π B2Σ
-161.1 +31.5 +40.6
-166.6 +10.8 +22.3
were carried out in the temperature ranges of respectively 3031038 K and 303-991 K. The experimental conditions together with all the values of k1Ca and k1Sr are listed in Table 1. The results can be fitted to the classical Arrhenius formalism according to eq 6:
k1Ca(Sr) ) A exp
( ) -Ea RT
(6)
in which A is the preexponential factor (cm3 molecule-1 s-1), Ea is the activation energy (kJ mol-1), R is the universal gas constant (8.31441 J mol-1 K-1), and T is the temperature (K). The rate constants k1Ca(Sr) were fitted to eq 6 by means of a
Reactions of Ca(1S) and Sr(1S) Atoms with Cl2
J. Phys. Chem. A, Vol. 104, No. 27, 2000 6409
TABLE 3: Comparison between the Calculated Values of rc, kej, and kmej (Equation 9) with the Value of rc(exp) Derived from kexp and the Experimental Value kexp at Room Temperature Ca/Cl2 (303 K) Sr/Cl2 (303 K)
rc (Å)
kej (cm3 molecule-1 s-1)
rc(exp) (Å)
kexp (cm3 molecule-1 s-1)
kmej (cm3 molecule-1 s-1)
2.8 3.1
1.2 × 10-10 1.2 × 10-10
5.9 6.6
5.4 × 10-10 5.6 × 10-10
7.7 × 10-10 6.6 × 10-10
weighted nonlinear regression using the SAS package,20 resulting in the following Arrhenius expressions:
k1Ca ) [(6.0 ( 0.8) × 10-10] × exp
(
k1Sr ) [(7.3 ( 0.6) × 10-10] × exp
)
-0.2 ( 0.5 kJ mol-1 cm3 molecule-1 s-1 (7) RT
(
)
-0.4 ( 0.4 kJ mol-1 cm3 molecule-1 s-1 (8) RT
The quoted error margins on both the preexponential factors and the Arrhenius activation energies are at the 1σ level. Figure 3 represents the values of ln k1Ca(Sr) from Table 1 versus 1/T. One sees that the rate constants are almost independent of the temperature and both eqs 7 and 8 show that the reactions are characterized by a small or even negligible activation energy in the range between 0.2 and 0.4 kJ mol-1 with an associated error of the same magnitude. Discussion The reaction enthalpies of the possible Ca(Sr)/Cl2 reactions are summarized in Table 212 and as one sees both reactions can only lead to ground-state CaCl and SrCl (X2Σ+) in view of the endothermicity of the other reactions. As already said the rate constants derived in this work can only be compared with the results of Kashireninov et al., obtained in the narrow temperature ranges between 990 and 1083 K for the Ca/Cl2 reaction and 933-1073 K for the Sr/Cl2 reaction.9 In both cases a small negative temperature dependence was observed (eqs 1 and 2). At the highest experimental temperatures covered in this work, i.e., 1038 K for the Ca/Cl2 reaction and 991 K for the Sr/Cl2 reaction, eqs 1 and 2 lead to values of k1Ca(Sr) respectively equal to 3.5 × 10-11 cm3 molecule-1 s-1 and 2.9 × 10-15 cm3 molecule-1 s-1. These values are respectively about 1 and 5 orders of magnitude lower than the second-order rate constants calculated from our data (eqs 7 and 8). In this context it should be mentioned that the derivation of kinetic data obtained by means of the TVDF (temperature variation of the diffusion flame) technique9 is strongly complicated due to several interferences as there are the high temperature gradients in the reaction zone, the occurrence of secondary reactions, and the influence of condensation of the gas-phase products onto the thermocouples. Another point is that their results were obtained in the narrow temperature range of about 150 K, which certainly diminuishes the reliability of the derived kinetic parameters. An attractive mechanism for interpretating the experimental results of the alkaline-earth-metal atom/Cl2 reactions is the electron-jump mechanism. The electron-jump distance rc with the corresponding rate constant kej can be calculated using the same expressions as given in our previous paper on the alkalineearth-metal atom/NO2 reactions.23 With the ionization energy IECa(Sr) of the Ca or Sr atoms, which is respectively equal to 6.10 and 5.69 eV, and the vertical electron affinity EAv(Cl2) of
the Cl2 molecule (1.0 eV),3 one can calculate the values for rc of the Ca(Sr)/Cl2 reactions: see Table 3. In the next step, the values of the electron-jump rate constants kej at, e.g., 303 K can be calculated and can then be compared with the experimental values at the same temperature. From Table 3 it is clear that for both reactions the electron-jump rate constant is about a factor of 5 lower than the experimental value. To explain these larger experimental values, long-range forces between the reacting species should be taken into account.24 These forces are mainly attractive dispersion forces which are active at distances larger than the electron-jump distance. This mechanism leads to a so-called modified electron-jump rate constant kmej which is given by eq 9: 25
km.e.j. ) π
( )( ) 2C6 RT
1/3
8RT πµ
1/2
Γ(2/3)cm3 molecule-1 s-1 (9)
in which Γ (2/3) is the gamma function of 2/3 ()1.354), T is the gas temperature, R is the universal gas constant ()1.38 × 10-23 J molecule-1 K-1), and µ is the reduced mass of the reacting species. In eq 9 the factor C6 only takes into account a dispersion disp for the Ca/Cl2 interaction Cdisp 6 . The derived values for C6 and the Sr/Cl2 reactions are respectively equal 1.0 × 10-16 and 1.2 × 10-16 J Å6 molecule-1. Since Cl2 has no permanent dipole moment, the dipole-induced component Cind 6 is equal to zero. Values of the rate constant kmej calculated at 303 K by means of eq 9 are also shown in Table 3. For the Ca(Sr)/Cl2 reactions they are respectively equal to 7.7 × 10-10 and 6.6 × 10-10 cm3 molecule-1 s-1. One sees that the modified electron-jump formalism, although it slightly overestimates kexp, better explains the magnitude of the rate constants than the classical electronjump formalism. In view of the very large value of the rate constants and the absence of any third-order character, one is allowed to estimate that chemiluminescence from the reaction sequence (4a-c) is unimportant for the overall destruction of the metal atoms in our experimental conditions. In the past also the Mg/Cl2 reaction has been investigated between 303 and 903 K using the same fast-flow reactor technique.17 Since the electron-jump distance rc (2.2 Å) at 303 K is about equal to the equilibrium bond length of the reaction product MgCl, a short distance charge-transfer rather than a clear electron-jump mechanism was postulated. In addition, at this short distance rc a repulsion on the potential energy surface already occurs, resulting in a low energy barrier for the Mg/Cl2 reaction of 3.6 ( 0.3 kJ mol-1. It needs to be pointed out that the observed activation energies of 0.2 ( 0.5 and 0.4 ( 0.4 kJ mol-1 for respectively the Ca and Sr reactions with Cl2 should be considered as negligible in view of the errors which are of the same magnitude (eqs 7 and 8). This observation is in qualitative agreement with the modified electron-jump mechanism, which implies the absence of an energy barrier. The large distances rc between 5.9 and 6.6 Å probably explains why the calculated reaction barriers on the basis of an approach of both reagents on a covalent potential energy surface will not be realistic. Acknowledgment. We thank the Fund for Joint Basic Research (FKFO), Brussels, Belgium, for a research grant. C.V.
6410 J. Phys. Chem. A, Vol. 104, No. 27, 2000 is a Research Director of the National Fund for Scientific Research (Belgium). J.H. is grateful to the Institute for Science and Technology (IWT) for granting her a doctoral fellowship. References and Notes (1) Polanyi, M. Atomic Reactions; Williams and Norgate, Ltd.: London, 1932. (2) Levy, M. R. Prog. React. Kinet. 1981, 10, 1. (3) Maya, J.; Davidovits, P. J. Chem. Phys. 1973, 59, 3143. (4) Maya, J.; Davidovits, P. J. Chem. Phys. 1974, 61, 1082. (5) Edelstein, S. A.; Davidovits, P. J. Chem. Phys. 1971, 55, 5164. (6) Magee, J. J. Chem. Phys. 1940, 8, 687. (7) Herschbach, D. R. AdV. Chem. Phys. 1966, 10, 319. (8) Honjou, N.; Yarkony, D. J. Phys. Chem. 1985, 89, 2919. (9) Kashireninov, O. E.; Manelis, G. B.; Repka, L. F. Russ. J. Phys. Chem. 1982, 56, 630. (10) Lin, S. M.; Mims, C. A.; Herm, R. R. J. Chem. Phys. 1973, 58, 327. (11) Gole, J. L.; Wang, H.; Joiner, J. S.; Dawson, D. E. J. Chem. Phys. 1995, 102, 19, 7437. (12) JANAF Thermochemical Tables. J. Phys. Chem. Ref. Data 1985, 14.
Vinckier et al. (13) Vinckier, C.; Christiaens, P.; Hendrickx, M. Gas-Phase Metal Reactions; Fontijn, A., Ed.; Elsevier: Amsterdam, 1992; p 57. (14) Vinckier, C.; Remeysen, J. J. Phys. Chem. 1994, 98, 10535. (15) Vinckier, C.; Helaers, J. J. Phys. Chem. A 1998, 102, 8333. (16) Vinckier, C.; Christiaens, P. J. Phys. Chem. 1992, 96, 2146. (17) Vinckier, C.; Christiaens, P. J. Phys. Chem. 1992, 96, 8423. (18) De Jaegere, S.; Willems, M.; Vinckier, C. J. Phys. Chem. 1982, 86, 3569. (19) Brouwers, H. Ph. D. Thesis, Faculty of Science, K. U. Leuven, 1984. (20) S. A. S. Statistical Package; S. A. S. Institute, Inc.: Cary, NC, 1989. (21) Fontijn, A.; Felder, W. ReactiVe Intermediates in the Gas-Phase, Generation and Monitoring; Setser, W., Ed.; Academic Press: New York, 1979; 59. (22) Vinckier, C.; Corthouts, J.; De Jaegere, S. J. Chem. Soc., Faraday Trans 2 1988, 84, 1951. (23) Vinckier, C.; Helaers; Christiaens, P.; Remeysen, J. J. Phys. Chem. A 1999, 103, 51, 11321. (24) Gislason, E. A. Alkali Halide Vapors; Davidovits, P., McFadden, D. L., Ed.; Academic Press: New York, 1979, 415. (25) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: London, 1980.
